Symmetry | |
Fermat Metrics | |
Antonio Masiello1  | |
[1] Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy; | |
关键词: Finsler metrics; stationary spacetimes; Fermat principle; light rays; critical point theory; | |
DOI : 10.3390/sym13081422 | |
来源: DOAJ |
【 摘 要 】
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.
【 授权许可】
Unknown